We answer this question in the context of U.S. cities, where women’s participation in mayoral elections increased from negligible numbers in 1970 to about one-third of the elections in the 2000’s....In contrast to most research on the influence of female leadership, we find no effect of gender of the mayor on policy outcomes related to the size of local government, the composition of municipal spending and employment, or crime rates.
What’s more, the authors continue, having a female mayor doesn’t make it any more likely that other female candidates will be elected to office, either for mayor or for Congress. That said, female mayors who manage to get elected are better at holding on to their seats.
“Female victors have superior political skills compared to otherwise equivalent males, as indicated by the fact that they are more likely to win elections once they are able to face the hurdle of winning the first election,” Ferreira and Gyourko write. “They have a 6-7 percentage point higher incumbent effect than a comparable male.”